Clustering of Conditional Mutual Information for Quantum Gibbs States above a Threshold Temperature

Tomotaka Kuwahara, Kohtaro Kato, and Fernando G. S. L. Brandão
Phys. Rev. Lett. 124, 220601 – Published 1 June 2020
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Abstract

We prove that the quantum Gibbs states of spin systems above a certain threshold temperature are approximate quantum Markov networks, meaning that the conditional mutual information decays rapidly with distance. We demonstrate the exponential decay for short-ranged interacting systems and power-law decay for long-ranged interacting systems. Consequently, we establish the efficiency of quantum Gibbs sampling algorithms, a strong version of the area law, the quasilocality of effective Hamiltonians on subsystems, a clustering theorem for mutual information, and a polynomial-time algorithm for classical Gibbs state simulations.

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  • Received 4 November 2019
  • Revised 31 January 2020
  • Accepted 8 May 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.220601

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsInterdisciplinary PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Tomotaka Kuwahara*

  • Mathematical Science Team, RIKEN Center for Advanced Intelligence Project (AIP),1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan and Interdisciplinary Theoretical & Mathematical Sciences Program (iTHEMS) RIKEN 2-1, Hirosawa, Wako, Saitama 351-0198, Japan

Kohtaro Kato

  • Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA

Fernando G. S. L. Brandão

  • Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA and Amazon Web Services, USA

  • *tomotaka.kuwahara@riken.jp
  • kokato@caltech.edu
  • fbrandao@caltech.edu

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Issue

Vol. 124, Iss. 22 — 5 June 2020

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